List of rotopes (no ontology)

From Hi.gher. Space

(Difference between revisions)
m (updated names of some obscure polychora)
m (toraspherinder -> torisphere, toracubinder -> spheritorus)
 
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|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''0D rotopes'''
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''0D rotopes'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Point (object)|Point]]'''
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Point]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''0'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''0'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Empty string'''''
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|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''1D rotopes'''
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''1D rotopes'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Line (object)|Line]]'''
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Line segment]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''1'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLL'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELLL'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid prism]]'''
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramidal prism]]'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''17'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''17'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xy<sup>z</sup>w'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''xy<sup>z</sup>w'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EETT'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''EETT'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramid torus]]'''
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Square pyramidal torus]]'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''19'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''19'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy<sup>z</sup>w)'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(xy<sup>z</sup>w)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELLT'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELLT'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toraspherinder]]'''
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Torisphere]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''22'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''22'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xyz)w)'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xyz)w)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETEE'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETEE'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prismidal pyramid]]'''
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Triangular prismic pyramid]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''24'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''24'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>z<sup>w</sup>'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>z<sup>w</sup>'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETET'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ETET'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular diprismidal torus]]'''
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Triangular prismic torus]]'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''25'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''25'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>zw)'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>zw)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETQQ'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ETQQ'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''''Unknown shape'''''
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cyltrianglinder]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''32'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''32'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>(zw)'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''x<sup>y</sup>(zw)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''''Unknown shape'''''
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Cyltrianglintigroid]]'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''33'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''33'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>(zw))'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''(x<sup>y</sup>(zw))'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELET'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELET'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Toracubinder]]'''
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Spheritorus]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''36'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''36'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)zw)'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''((xy)zw)'''
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|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELTT'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''ELTT'''
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|-
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Conindral torus]]'''
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|valign="top" width="20%" style="background-color:#ccccff; text-align:center;"|'''[[Conic torus]]'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''39'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''39'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((xy)<sup>z</sup>w)'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''((xy)<sup>z</sup>w)'''
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|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELQT'''
|valign="top" width="16%" style="background-color:#ddddff; text-align:center;"|'''ELQT'''
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|-
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Tetratorus]]'''
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|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Ditorus]]'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''42'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''42'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(((xy)z)w)'''
|valign="top" width="16%" style="background-color:#eeeeff; text-align:center;"|'''(((xy)z)w)'''
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[[Category:Rotopes|$]]
[[Category:Rotopes|$]]
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[[Category:Lists|Rotopes]]
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[[Category:Lists of shapes|Rotopes]]

Latest revision as of 19:50, 2 February 2014

This is a list of rotopes in dimensions from zero to four.

Name Rotopic index Group notation Digit notation Product notation CSG notation
0D rotopes
Point 0 Empty string Empty string 0 Empty string
1D rotopes
Line segment 1 x 1 1 E
2D rotopes
Square 2 xy 11 1x1 EE
Triangle 3 xy 11 1~0 ET
Circle 4 (xy) 2 2 EL
3D rotopes
Cube 5 xyz 111 1x1x1 EEE
Square pyramid 6 xyz 111 (1x1)~0 EET
Sphere 7 (xyz) 3 3 ELL
Triangular prism 8 xyz 111 (1~0)x1 ETE
Tetrahedron 9 xyz 12 1~0~0 ETT
Triangular torus 10 (xyz) (111) 2#(1~0) ETQ
Cylinder 11 (xy)z 21 2x1 ELE
Cone 12 (xy)z 21 2~0 ELT
Torus 13 ((xy)z) (21) 2#2 ELQ
4D rotopes
Tesseract 14 xyzw 1111 1x1x1x1 EEEE
Cubic pyramid 15 xyzw 1111 (1x1x1)~0 EEET
Glome 16 (xyzw) 4 4 ELLL
Square pyramidal prism 17 xyzw 1111 ((1x1)~0)x1 EETE
Square dipyramid 18 xyzw 112 (1x1)~0~0 EETT
Square pyramidal torus 19 (xyzw) (1111) ((1x1)~0)#2 EETQ
Spherinder 20 (xyz)w 31 3x1 ELLE
Sphone 21 (xyz)w 31 3~0 ELLT
Torisphere 22 ((xyz)w) (31) 3#2 ELLQ
Triangular diprism 23 xyzw 1111 (1~0)x1x1 ETEE
Triangular prismic pyramid 24 xyzw 1111 ((1~0) x1)~0 ETET
Triangular prismic torus 25 (xyzw) (1111) 2#((1~0) x1) ETEQ
Tetrahedral prism 26 xyzw 121 (1~0~0) x1 ETTE
Pentachoron 27 xyzw 13 1~0~0~0 ETTT
Tetrahedral torus 28 (xyzw) (121) 2#(1~0~0) ETTQ
Triangular toric prism 29 (xyz)w (111)1 2#(1~0) x1 ETQE
Triangular toric pyramid 30 (xyz)w (111)1 (2#(1~0)) ~0 ETQT
Triangular ditorus 31 ((xyz)w) ((111)1) 2#(2#(1~0)) ETQQ
Cyltrianglinder 32 xy(zw) 112 Unknown Unknown
Cyltrianglintigroid 33 (xy(zw)) (112) Unknown Unknown
Cubinder 34 (xy)zw 211 2x1x1 ELEE
Cylindrical pyramid 35 (xy)zw 211 (2x1)~0 ELET
Spheritorus 36 ((xy)zw) (211) 2#3 ELEQ
Coninder 37 (xy)zw 211 (2~0)x1 ELTE
Dicone 38 (xy)zw 22 2~0~0 ELTT
Conic torus 39 ((xy)zw) (211) 2#(2~0) ELTQ
Torinder 40 ((xy)z)w (21)1 (2#2)x1 ELQE
Toric pyramid 41 ((xy)z)w (21)1 (2#2)~0 ELQT
Ditorus 42 (((xy)z)w) ((21)1) (2#2)#2 ELQQ
Duocylinder 43 (xy)(zw) 22 2x2 EL*EL
Tiger 44 ((xy)(zw)) (22) (2x2)#2 Unknown
Retrieved from "http://hi.gher.space/wiki/List_of_rotopes"